The big clue is in the yellow box in the middle "No device detected" which means just that. The error isn't that it read back the wrong device ID, it's that it didn't read anything back at all!
The reason it shows 3FE0 is because that's the standard bit mask for device IDs. In binary it is 0011 1111 1110 0000, when you consider the leftmost two bits are always zero and the silicon revision is stored inthe right most 5 bits, it leaves the middle '1' bits as the device type identifier. The mask is ANDed with the bytes read from the PIC so it only sees the ID and not the silicon revision. In your case it effectively read nothing and the result was 1111 1111 1111 1111 which ANDed with the mask results in 3FE0.
Your real problem is either in the wiring between the Pickit2 and the PIC or, if it not a real Microchip one but a clone, the power rails are inadequate. If you are trying to program it while the PIC is connected to another circuit, check it meets the requirements as specified in the Pickit2 manual.
I have several Pickit2 programmers and they work hard programming hundreds of PICs, including 16F628A and I have never had a single failure.
Brian.